From a72ed3f8301b493dfbaad82a2f4dabd4cc0b78f2 Mon Sep 17 00:00:00 2001
From: Donovan <donovan.a.kelly@pm.me>
Date: Fri, 28 Jun 2024 09:37:01 -0500
Subject: [PATCH] refactor readme

---
 README.md          | 80 +++++++++++++++++++++++++++++++---------------
 src/client_darc.py | 10 ++++++
 2 files changed, 64 insertions(+), 26 deletions(-)

diff --git a/README.md b/README.md
index 5fa74ba..463e5ea 100644
--- a/README.md
+++ b/README.md
@@ -2,39 +2,67 @@
 
 ### translate data 
 ```
-alpha_phase_1 = si1_mo3(so1[alphabet]) ^ mi1_mo2(mo1[s_a ^ m_a ^ se_a])
+alpha_phase1 = (
+        ((alphabet < sdo1) << (sdi1 < mdo3)) ^
+        (((spda ^ seda) < mdo1) << (mdi1 < mdo2))
+)
 ```
 
 ### receive alphabet
-recall: 
-- `server_persistent_key.alpha = s_a ^ m_a`
-- `mutual_persistent_key.alpha = m_a ^ c_a`
-- `client_persistent_key.alpha = c_a`
 ```
-result = alpha_phase_1 ^ mi1_mo2(mo1[ce_a ^ c_a ^ m_a ^ c_a])
-result = alpha_phase_1 ^ mi1_mo2(mo1[ce_a ^ m_a]) # c_a cancels
-result = si1_mo3(so1[alphabet]) ^ mi1_mo2(mo1[s_a ^ m_a ^ se_a]) ^ mi1_mo2(mo1[ce_a ^ m_a]) # expand alpha phase 1
-result = si1_mo3(so1[alphabet]) ^ mi1_mo2(mo1[s_a ^ se_a ^ ce_a]) # client_ephemeral_alpha added and m_a cancels
-expr1 = result
-
-alpha_phase_2 = mo3_co1_co2[ci1(nmo3[expr1])]
+alphabet_phase2 = ((((
+    alphabet_phase1 ^
+    (((ceda ^ cpda ^ mpda) < mdo1) << (mdi1 < mdo2))
+) < ~mdo3)) << cdi1) < (mdo3 << cdo1 << cdo2)
+```
+#### Replace Alphabet Phase 1
+```
+alphabet_phase2 = ((((
+    ((alphabet < sdo1) << (sdi1 < mdo3)) ^
+    (((spda ^ seda) < mdo1) << (mdi1 < mdo2)) ^
+    (((ceda ^ cpda ^ mpda) < mdo1) << (mdi1 < mdo2))
+) < ~mdo3)) << cdi1) < (mdo3 << cdo1 << cdo2)
+```
+#### Simplified Expression
+```
+alphabet_phase2 = ((((
+    ((alphabet < sdo1) << (sdi1 < mdo3)) ^
+    (((ceda ^ cpda ^ mpda ^ spda ^ seda) < mdo1) << (mdi1 < mdo2))
+) < ~mdo3)) << cdi1) < (mdo3 << cdo1 << cdo2)
 ```
 
+recall:
+- `spda = s_a ^ m_a`
+- `mpda = m_a ^ c_a`
+- `cpda = c_a`
+
+#### Final Alphabet Phase 2 
+```
+alphabet_phase2 = ((((
+    ((alphabet < sdo1) << (sdi1 < mdo3)) ^
+    (((ceda ^ s_a ^ seda) < mdo1) << (mdi1 < mdo2))
+) < ~mdo3)) << cdi1) < (mdo3 << cdo1 << cdo2)
+```
 ### transmit alphabet
+```
+alphabet_phase3 = (
+    (alphabet_phase2 << ((~cdi1 << mdpi2) < (mdo3 << cdo1 << cdo2))) ^
+    ((((ceda ^ cpda ^ meda) < mdo1) << ((mdi1 < mdo2) << (mdpi2 < mdo3))) < (cdo1 << cdo2))
+)
+```
+
+#### Distribute cdo1 << cdo2 term and replace alphabet_phase2
 
 ```
-result = nceil_ncpi1_mpi2_mo3_co1_co2(alpha_phase_2)
-result = nceil_ncpi1_mpi2_mo3_co1_co2(mo3_co1_co2[ci1(nmo3[expr1])])
-result = mo3_co1_co2[nceil_ncpi1_mpi2(ci1(nmo3[expr1]))]
-result = mo3_co1_co2[mpi2(nmo3[expr1])]
-result = mo3_co1_co2[mpi2(nmo3[ si1_mo3(so1[alphabet]) ^ mi1_mo2(mo1[s_a ^ se_a ^ ce_a])])]
-result = mo3_co1_co2[mpi2(si1(so1[alphabet]) ^ nmo3[mi1_mo2(mo1[s_a ^ se_a ^ ce_a])])]
-
-alpha_phase_3 = result ^ co1_co2[mi1_mo2_mpi2_mo3(mo1[ce_a ^ c_a ^ m_a ^ c_a])]
-alpha_phase_3 = result ^ co1_co2[mi1_mo2_mpi2_mo3(mo1[ce_a ^ m_a])]
-
-alpha_phase_3 = mo3_co1_co2[mpi2(si1(so1[alphabet]) ^ nmo3[mi1_mo2(mo1[s_a ^ se_a ^ ce_a])])] ^ co1_co2[mi1_mo2_mpi2_mo3(mo1[ce_a ^ m_a])]
-
-alpha_phase_3 = co1_co2[ si1_mpi2_mo3(so1[alphabet]) ^ mi1_mo2_mpi2_mo3(mo1[s_a ^ se_a ^ ce_a])  ^ mi1_mo2_mpi2_mo3(mo1[ce_a ^ m_a])]
-alpha_phase_3 = co1_co2[ si1_mpi2_mo3(so1[alphabet]) ^ mi1_mo2_mpi2_mo3(mo1[s_a ^ se_a ^ m_a])] 
+alphabet_phase3 = (
+    ((
+        (alphabet_phase2 << ((~cdi1 << mdpi2) < (mdo3 << cdo1 << cdo2))) ^
+        ((((ceda ^ cpda ^ meda) < mdo1) << ((mdi1 < mdo2) << (mdpi2 < mdo3))) < (cdo1 << cdo2))
+    ) << ((~cdi1 << mdpi2) < (mdo3 << cdo1_cdo2))) ^
+        (
+            (
+                ((ceda ^ cpda ^ meda) < (mdo1 << cdo1 << cdo2)) << ((mdi1 < (mdo2 << cdo1 << cdo2)) << (mdpi2 < (mdo3 << cdo1 << cdo2)))
+            )
+        )
+)
 ```
\ No newline at end of file
diff --git a/src/client_darc.py b/src/client_darc.py
index 04916f2..69e510b 100644
--- a/src/client_darc.py
+++ b/src/client_darc.py
@@ -113,6 +113,16 @@ def transmit_alphabet(
             (alphabet_phase2 << ((~cdi1 << mdpi2) < (mdo3 << cdo1_cdo2))) ^
             ((((ceda ^ cpda ^ meda) < mdo1) << ((mdi1 < mdo2) << (mdpi2 < mdo3))) < cdo1_cdo2)
     )
+
+
+    alphabet_phase3 = (
+            (alphabet_phase2 << ((~cdi1 << mdpi2) < (mdo3 << cdo1_cdo2))) ^
+            (
+                    (
+                            ((ceda ^ cpda ^ meda) < (mdo1 << cdo1_cdo2)) << ((mdi1 < (mdo2 << cdo1_cdo2)) << (mdpi2 < (mdo3 << cdo1_cdo2)))
+                    )
+            )
+    )
     return alphabet_phase3